In many signal processing systems, particularly those which employ one or more transducers that are subject to anomalous inputs from their observation environment, the signal waveform of interest may be impacted by randomly occurring noise impulses or artifacts having a peak amplitude that may be orders of magnitude in excess of that of the expected waveform and have extremely fast rise and fall times compared to the rate of change of the signal of the monitored signal. One non-limitative example is the contamination of low level electrical signal currents by large exponentially distributed amplitude current spikes, which may be Poisson-distributed in time on the input waveform. In such a case, it can be shown that the mean and variance of displaced electrons due to noise impulses are given by the expressions: EQU Mi=nNo, and (1) ##EQU1## where
Mi=Mean number of displaced electrons, PA1 .sigma.i=Standard deviation of displaced electrons, PA1 No=Average number of electrons in a set of impulses, and PA1 n=Probability that an impulse occurs in a given time interval. PA1 t.sub.i =detector integration time, PA1 g=noise flux density, and PA1 k.sub.s =scattering factor.
The quantities No and n are dependent on many factors relating to the physical nature of the noise source, with typical values for No being 20,000 to 40,000 electrons. The value of n, on the other hand, is a function of the physical design of the sensing system utilized. For an optoelectronic transducer having a focal plane detector area of Ad, the value on n may be defined as: EQU n=Adt.sub.i gk.sub.s ( 3)
where:
The variable t.sub.i requires further explanation. A conventional technique of converting low level currents to signal voltages is to integrate the current for a fixed length of time (t.sub.i). The output voltage is directly proportional to the current and integration time. This method of transimpedance amplification is known as reset integration. As can be seen from equation (3), the longer the integration time, the more likely a noise contaminated pulse will occur. The scattering factor ks is a function of the configuration of the detector.
Typical values of n range from 0.1 to 0.5. A value of n=0.1 implies that out of ten sequential time periods of length t.sub.i, one time period on the average will contain an impulse of noise current. Based on these values along with assumed numbers for No, a range of induced noise levels can be defined using equations (1) and (2), as: EQU 2000&lt;Mi&lt;20,000 (electrons),and EQU 9000&lt;.sigma.i&lt;40,000 (electrons).
Signal detection in many applications requires resolution of as few as 300 electrons in an integration time interval. Obviously, with noise levels of 9000 electrons, a method of noise (impulse) attenuation is necessary if successful detection is to take place. Further, since sensor system amplifications imply large numbers of input signals, the method employed must be efficient.
With reference to equation (3), one conventional method of impulse noise reduction is to minimize detector area and shorten the integration time of the transimpedance amplifier. This will reduce the event rate but have little effect on the impulse amplitude. Generally, for very small signal currents, this technique has proven inadequate.
A second method, diagrammatically shown in FIG. 1, involves connecting a simple low pass filter 2 at the output of a transimpedance amplifier 1. Since a transimpedance amplifier is a sampling circuit (it is periodically reset to begin a new integration period), the low pass filter may be a sampled data filter implemented with switched capacitor components. It can be shown that the noise at the output of the low pass filter may be defined by the expressions: EQU Mo=nNo, and (4) ##EQU2## where Mo and .sigma.o are output mean and standard deviation of the noise, fc is the filter cut-off frequency and fs is the reset sampling frequency equal to 1/t.sub.i. The value of fc is set by the desired signal bandwidth. In cases where the signal bandwidth is much less than the impulse event rate, comparing equation (5) to equation (2) reveals a significant amount of attenuation. This method works well if fc can be made small as compared to fs.
A third approach centers around a digital processing solution, diagrammatically illustrated in FIG. 2. Since there are N multiple diodes in a photodetector array, the outputs of their associated transimpedance amplifiers 1-1 . . . 1-N are sampled via respective sample and hold circuits 3-1 . . . 3-N and selectively coupled by way of a multiplexer 4 to an analog-digital converter (ADC) 5 (or set of ADCs if parallel processing is used). Each channel is digitally demultiplexed in demultiplexer 6 and the following sequence of steps (S1)-(S6) is carried out within an associated digital processor 7 to remove impulse noise.
(S1) N consecutive samples are retained from each detector;
(S2) Compare the N samples and choose the smallest value (assuming that it is free of contamination (due to impulse noise);
(S3) Add a small value Vo representative of system thermal noise to the smallest sample to generate a signal threshold Vt;
(S4) Compare each sample value Vs to the threshold Vt;
(S5) Discard the samples exceeding the threshold; and
(S6) Sum the remaining samples to enhance signal gain.
Although this technique can provide significant reduction in impulse noise, its implementation suffers from a number of problems. First of all, it is necessary that the sampling rate be fast enough to prevent one or more samples from being contaminated with noise impulses. For a large numbers of detectors this places an enormous burden on the A-D converter. For example, a 128.times.128 diode array sampled at 10 KHz requires an analog to digital conversion rate of 163.84 MHz. If twelve bit resolution is required (which is typical), such a converter is well beyond the current state of the art. While parallel processing is possible, the number of A-D converters may be prohibitively large and unreasonable due to size constraints. The output data rate at the multiplexer would be very high, as well placing a very difficult settling requirement on the output driver. Combining the data rate requirement and number of A-D converters necessary would result in substantial power dissipation, which is highly undesirable in environments such as focal plane arrays where cold temperatures must be maintained.
A third problem relates to the digital storage required to implement the process. Further, the digital processor must run at rates consistent with noise contamination rather than at the Nyquist rate of the desired signal. Finally, since the uncontaminated samples are summed as the last step (S6) of the process, the overall gain of the system is dependent upon the statistics of the noise This implies the need for an additional correction mechanism, which further complicates the process.